四元数矩阵特征值的两个定理  

Two Theorems for the Eigenvalue of Quaternion Matrix

作　　者：胡青龙[1] 盛秀艳[2] 

机构地区：[1]西昌学院工程技术系,四川西昌615013 [2]聊城大学数学科学学院,山东聊城252059

出　　处：《绵阳师范学院学报》2009年第11期12-14,18,共4页Journal of Mianyang Teachers＇ College

摘　　要：爱尔兰数学家哈密顿于1843年发现了四元数。实四元数矩阵研究的主要难点在于四元数乘法的不可交换性。四元数在众多的应用问题中扮演着重要的角色,如计算机图形图像处理。该文的目的在于讨论自共轭四元数矩阵特征值的不等式。基于自共轭四元数矩阵的酉对角化和体上矩阵的运算,得到了四元数正定矩阵特征值的两个定理。Quaternion was introduced by Irish mathematician Hamilton in 1843. It is well - known that the main obstacle in the study of quaternion matrices is the non - commutation multiplication of quaternion. There is wide- ranging connection with many applied science, such as the figure and pattern recognition. The purpose of this paper is to discuss the inequalities of self - conjugate quaternion matrix. The authors present two theorems for the eigenvalue of quaternion positive definite matrices based on unitary diagonalizability and the operation of quaternion matrices.

关 键 词：四元数矩阵 特征值 范数 

分 类 号：O241.6[理学—计算数学]